Why did Hanuman stay on Arjuna’s chariot but never actually join the fight?

 Hanuman is Vayuputra, and Bheem was also Vayuputra from different yugas. Hanuman fought in treta yuga with lord Rama against the Lankan Asura army. His task as a great warrior was accomplished in that yuga. His next big task is during the Kali Yuga, to be the frontline general against the ultra-powerful demon Kali. He is one of the seven Chiranjeevis, who will defeat the demon Kali to end this adharmic yuga.

As he is from the Treta Yuga, he is more powerful than the warriors of the Dwapara Yuga and could end the war in a few days, single-handedly. But destiny has it that he shouldn't engage in the Great War and instead increase his power for the final battle with Kali. till then, he is meditating and increasing his power in the Dwapar and this Yuga.

bheem engaged in the Kurukshetra war against the Kauravas in the Dwapar Yuga. he met Hanuman during his vanavaas and gained his trust for the support during the war. Hanuman, being of the same divine birth, agreed to be present with bheem in the war, in an invisible energy form. And to protect Arjuna, he took form in arjunas flag on his chariot.

Why did he take Arjuna's place and not Bheem's is an interesting question. Bheem had vowed to vanquish all 100 kauravas through his physical strength, but Arjuna had a greater role in vanquishing the powerful astras wielded by powerful warriors such as Aswathama, Karna, Drona and Bheesma. If Arjuna was injured and out of action, the Pandava army didn't possess the astras to defeat their enemies. He needed protection from Brahmastra, Bhargavastra, Narayanastra etc. Hence, he took Arjuana's flag instead of bheemas.

Which small screen actor could best portray Arjuna?

 Arjun supposed to have dark complexion and his age was said to be more than 70 years old.

In terms of looks - Navi Bhangu had dark complexion did a decent job he had good screen presence and warrior look.He played Brihannala very well in Suryaputra Karn series. His costumes were also good.

Shaheer Sheikh didn't look like Arjuna. He look like lover boy and chocolate boy. So I didn't like his role as Arjuna. However his comedy timings and interactions with other actors in the character is enjoyable to watch. So he is good Arjuna in terms of comedy timings and romantic timings.

In terms of dialogue delivery and acting skills -Firoz Khan did excellent job as Arjuna or Partha but his costumes were worst. Infact all of BR Chopra's serials had worst costumes. They look like cardboards rather than metal armors.

Why did Karna hate Pandavas? Why was he so obsessed with defeating Arjun?

 Hatred n’ at opposite ends may not mean the same. They were aligned at opposite poles by virtue of their birth.

Karna was against apartheid of the Royal Kingdom n’ their entourage who right from birth humiliated him for being a Shudra Putra or a Suta Putra, an offensive term indicating racial profiling.

The Blue blooded guys looked down on their race and defined limits to their occupational and professional rights, including freedom of speech. Pretty much serfdom!

In 21st Century, in a country like India where the Epic originated, the Law elucidates, you could end up in prison for the rest of the life by merely using the “clan” word. Such was the dread! That model hasn't changed. So the other segment has to zip up and endure in silence for trepidation of repercussions!

Putting into perspective, imagine the kinda life Karna led right from being discarded at birth and the barriers at every step. As if he had no right to live being a Suta Putra. Before you judge Karna, fathom one's own self today in a verisimilitude of sitch.

For Karna, that speaketh of, at every step, every breath he took, every decision he had to make was toxic!

His merit was dishonored, skills purged, education denied. As if that weren't enough, incessant humiliation.

The injustice unto lower clans by virtue of Royal prerogatives was too much for him to take. Eklavya for instance, was shunned from practice of Archery. They took away his thumb!

Karna was given no opportunity to prove his worth ever.

He wasn't a lower clan guy either. He was divine. His point was there should be equanimity of laws, recognition of merit, liberty to choose your occupation and a coherent justice system. The Kshatriyas as they were called liked to decide everything for the hoipolloi. They called the shots. They controlled the bureaucracy of all, including Pandits in an autocratic law that they formulated.

On the other end, were the Pandavas who embraced the Royal Shroud of supremacy, availing the leverage of all benefits. Arjuna, who constantly boasted of his supremacy miffed Karna! He was of the purview others should be evaluated before reaching a judgement.

Education, Occupation, Profession should be based on Merit, not by virtue of what your race is. It should be your deeds, Karmas that should be the governing factor.

This systematic demarcation, isolation is ADHARMA!

Only Duryodhana stood by Karna, who incidentally was at loggerheads with Pandavas. And there's that loyalty, allegiant factor that defines a COMPLETE MAN! Karna picked his Dharma as per the loci of the vicissitudes of his life!